That's the badge that was on mine when I bought it, similar to yours the other one fell off. Must be a thing about right hand tank badges! Seems a bit of a grey area tanks and badges on BSA's around 1960, round / teardrop, silver / gold / black.
One piece of advice if you replace them is make sure the new ones are of decent quality and ethanol proof.
The ones I bought from rectoryantiques17 on FleaBay a few years ago were not good quality as you can see after the first time I overfilled the tank a few months later. After I complained to the seller his help was to ban me from his FleaBay shop which remains the case today as I have just checked. The other give-away was the poorly formed lettering, look at the cut-outs on the "B".